Polytope of Type {18,38}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {18,38}*1368
Also Known As : {18,38|2}. if this polytope has another name.
Group : SmallGroup(1368,59)
Rank : 3
Schlafli Type : {18,38}
Number of vertices, edges, etc : 18, 342, 38
Order of s0s1s2 : 342
Order of s0s1s2s1 : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {6,38}*456
   9-fold quotients : {2,38}*152
   18-fold quotients : {2,19}*76
   19-fold quotients : {18,2}*72
   38-fold quotients : {9,2}*36
   57-fold quotients : {6,2}*24
   114-fold quotients : {3,2}*12
   171-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   None.

Permutation Representation (GAP) : 
s0 := (  2,  3)(  5,  6)(  8,  9)( 11, 12)( 14, 15)( 17, 18)( 20, 21)( 23, 24)( 26, 27)( 29, 30)( 32, 33)( 35, 36)( 38, 39)( 41, 42)( 44, 45)( 47, 48)( 50, 51)( 53, 54)( 56, 57)( 58,116)( 59,115)( 60,117)( 61,119)( 62,118)( 63,120)( 64,122)( 65,121)( 66,123)( 67,125)( 68,124)( 69,126)( 70,128)( 71,127)( 72,129)( 73,131)( 74,130)( 75,132)( 76,134)( 77,133)( 78,135)( 79,137)( 80,136)( 81,138)( 82,140)( 83,139)( 84,141)( 85,143)( 86,142)( 87,144)( 88,146)( 89,145)( 90,147)( 91,149)( 92,148)( 93,150)( 94,152)( 95,151)( 96,153)( 97,155)( 98,154)( 99,156)(100,158)(101,157)(102,159)(103,161)(104,160)(105,162)(106,164)(107,163)(108,165)(109,167)(110,166)(111,168)(112,170)(113,169)(114,171)(173,174)(176,177)(179,180)(182,183)(185,186)(188,189)(191,192)(194,195)(197,198)(200,201)(203,204)(206,207)(209,210)(212,213)(215,216)(218,219)(221,222)(224,225)(227,228)(229,287)(230,286)(231,288)(232,290)(233,289)(234,291)(235,293)(236,292)(237,294)(238,296)(239,295)(240,297)(241,299)(242,298)(243,300)(244,302)(245,301)(246,303)(247,305)(248,304)(249,306)(250,308)(251,307)(252,309)(253,311)(254,310)(255,312)(256,314)(257,313)(258,315)(259,317)(260,316)(261,318)(262,320)(263,319)(264,321)(265,323)(266,322)(267,324)(268,326)(269,325)(270,327)(271,329)(272,328)(273,330)(274,332)(275,331)(276,333)(277,335)(278,334)(279,336)(280,338)(281,337)(282,339)(283,341)(284,340)(285,342);;
s1 := (  1, 58)(  2, 60)(  3, 59)(  4,112)(  5,114)(  6,113)(  7,109)(  8,111)(  9,110)( 10,106)( 11,108)( 12,107)( 13,103)( 14,105)( 15,104)( 16,100)( 17,102)( 18,101)( 19, 97)( 20, 99)( 21, 98)( 22, 94)( 23, 96)( 24, 95)( 25, 91)( 26, 93)( 27, 92)( 28, 88)( 29, 90)( 30, 89)( 31, 85)( 32, 87)( 33, 86)( 34, 82)( 35, 84)( 36, 83)( 37, 79)( 38, 81)( 39, 80)( 40, 76)( 41, 78)( 42, 77)( 43, 73)( 44, 75)( 45, 74)( 46, 70)( 47, 72)( 48, 71)( 49, 67)( 50, 69)( 51, 68)( 52, 64)( 53, 66)( 54, 65)( 55, 61)( 56, 63)( 57, 62)(115,116)(118,170)(119,169)(120,171)(121,167)(122,166)(123,168)(124,164)(125,163)(126,165)(127,161)(128,160)(129,162)(130,158)(131,157)(132,159)(133,155)(134,154)(135,156)(136,152)(137,151)(138,153)(139,149)(140,148)(141,150)(142,146)(143,145)(144,147)(172,229)(173,231)(174,230)(175,283)(176,285)(177,284)(178,280)(179,282)(180,281)(181,277)(182,279)(183,278)(184,274)(185,276)(186,275)(187,271)(188,273)(189,272)(190,268)(191,270)(192,269)(193,265)(194,267)(195,266)(196,262)(197,264)(198,263)(199,259)(200,261)(201,260)(202,256)(203,258)(204,257)(205,253)(206,255)(207,254)(208,250)(209,252)(210,251)(211,247)(212,249)(213,248)(214,244)(215,246)(216,245)(217,241)(218,243)(219,242)(220,238)(221,240)(222,239)(223,235)(224,237)(225,236)(226,232)(227,234)(228,233)(286,287)(289,341)(290,340)(291,342)(292,338)(293,337)(294,339)(295,335)(296,334)(297,336)(298,332)(299,331)(300,333)(301,329)(302,328)(303,330)(304,326)(305,325)(306,327)(307,323)(308,322)(309,324)(310,320)(311,319)(312,321)(313,317)(314,316)(315,318);;
s2 := (  1,175)(  2,176)(  3,177)(  4,172)(  5,173)(  6,174)(  7,226)(  8,227)(  9,228)( 10,223)( 11,224)( 12,225)( 13,220)( 14,221)( 15,222)( 16,217)( 17,218)( 18,219)( 19,214)( 20,215)( 21,216)( 22,211)( 23,212)( 24,213)( 25,208)( 26,209)( 27,210)( 28,205)( 29,206)( 30,207)( 31,202)( 32,203)( 33,204)( 34,199)( 35,200)( 36,201)( 37,196)( 38,197)( 39,198)( 40,193)( 41,194)( 42,195)( 43,190)( 44,191)( 45,192)( 46,187)( 47,188)( 48,189)( 49,184)( 50,185)( 51,186)( 52,181)( 53,182)( 54,183)( 55,178)( 56,179)( 57,180)( 58,232)( 59,233)( 60,234)( 61,229)( 62,230)( 63,231)( 64,283)( 65,284)( 66,285)( 67,280)( 68,281)( 69,282)( 70,277)( 71,278)( 72,279)( 73,274)( 74,275)( 75,276)( 76,271)( 77,272)( 78,273)( 79,268)( 80,269)( 81,270)( 82,265)( 83,266)( 84,267)( 85,262)( 86,263)( 87,264)( 88,259)( 89,260)( 90,261)( 91,256)( 92,257)( 93,258)( 94,253)( 95,254)( 96,255)( 97,250)( 98,251)( 99,252)(100,247)(101,248)(102,249)(103,244)(104,245)(105,246)(106,241)(107,242)(108,243)(109,238)(110,239)(111,240)(112,235)(113,236)(114,237)(115,289)(116,290)(117,291)(118,286)(119,287)(120,288)(121,340)(122,341)(123,342)(124,337)(125,338)(126,339)(127,334)(128,335)(129,336)(130,331)(131,332)(132,333)(133,328)(134,329)(135,330)(136,325)(137,326)(138,327)(139,322)(140,323)(141,324)(142,319)(143,320)(144,321)(145,316)(146,317)(147,318)(148,313)(149,314)(150,315)(151,310)(152,311)(153,312)(154,307)(155,308)(156,309)(157,304)(158,305)(159,306)(160,301)(161,302)(162,303)(163,298)(164,299)(165,300)(166,295)(167,296)(168,297)(169,292)(170,293)(171,294);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) : 
F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(342)!(  2,  3)(  5,  6)(  8,  9)( 11, 12)( 14, 15)( 17, 18)( 20, 21)( 23, 24)( 26, 27)( 29, 30)( 32, 33)( 35, 36)( 38, 39)( 41, 42)( 44, 45)( 47, 48)( 50, 51)( 53, 54)( 56, 57)( 58,116)( 59,115)( 60,117)( 61,119)( 62,118)( 63,120)( 64,122)( 65,121)( 66,123)( 67,125)( 68,124)( 69,126)( 70,128)( 71,127)( 72,129)( 73,131)( 74,130)( 75,132)( 76,134)( 77,133)( 78,135)( 79,137)( 80,136)( 81,138)( 82,140)( 83,139)( 84,141)( 85,143)( 86,142)( 87,144)( 88,146)( 89,145)( 90,147)( 91,149)( 92,148)( 93,150)( 94,152)( 95,151)( 96,153)( 97,155)( 98,154)( 99,156)(100,158)(101,157)(102,159)(103,161)(104,160)(105,162)(106,164)(107,163)(108,165)(109,167)(110,166)(111,168)(112,170)(113,169)(114,171)(173,174)(176,177)(179,180)(182,183)(185,186)(188,189)(191,192)(194,195)(197,198)(200,201)(203,204)(206,207)(209,210)(212,213)(215,216)(218,219)(221,222)(224,225)(227,228)(229,287)(230,286)(231,288)(232,290)(233,289)(234,291)(235,293)(236,292)(237,294)(238,296)(239,295)(240,297)(241,299)(242,298)(243,300)(244,302)(245,301)(246,303)(247,305)(248,304)(249,306)(250,308)(251,307)(252,309)(253,311)(254,310)(255,312)(256,314)(257,313)(258,315)(259,317)(260,316)(261,318)(262,320)(263,319)(264,321)(265,323)(266,322)(267,324)(268,326)(269,325)(270,327)(271,329)(272,328)(273,330)(274,332)(275,331)(276,333)(277,335)(278,334)(279,336)(280,338)(281,337)(282,339)(283,341)(284,340)(285,342);
s1 := Sym(342)!(  1, 58)(  2, 60)(  3, 59)(  4,112)(  5,114)(  6,113)(  7,109)(  8,111)(  9,110)( 10,106)( 11,108)( 12,107)( 13,103)( 14,105)( 15,104)( 16,100)( 17,102)( 18,101)( 19, 97)( 20, 99)( 21, 98)( 22, 94)( 23, 96)( 24, 95)( 25, 91)( 26, 93)( 27, 92)( 28, 88)( 29, 90)( 30, 89)( 31, 85)( 32, 87)( 33, 86)( 34, 82)( 35, 84)( 36, 83)( 37, 79)( 38, 81)( 39, 80)( 40, 76)( 41, 78)( 42, 77)( 43, 73)( 44, 75)( 45, 74)( 46, 70)( 47, 72)( 48, 71)( 49, 67)( 50, 69)( 51, 68)( 52, 64)( 53, 66)( 54, 65)( 55, 61)( 56, 63)( 57, 62)(115,116)(118,170)(119,169)(120,171)(121,167)(122,166)(123,168)(124,164)(125,163)(126,165)(127,161)(128,160)(129,162)(130,158)(131,157)(132,159)(133,155)(134,154)(135,156)(136,152)(137,151)(138,153)(139,149)(140,148)(141,150)(142,146)(143,145)(144,147)(172,229)(173,231)(174,230)(175,283)(176,285)(177,284)(178,280)(179,282)(180,281)(181,277)(182,279)(183,278)(184,274)(185,276)(186,275)(187,271)(188,273)(189,272)(190,268)(191,270)(192,269)(193,265)(194,267)(195,266)(196,262)(197,264)(198,263)(199,259)(200,261)(201,260)(202,256)(203,258)(204,257)(205,253)(206,255)(207,254)(208,250)(209,252)(210,251)(211,247)(212,249)(213,248)(214,244)(215,246)(216,245)(217,241)(218,243)(219,242)(220,238)(221,240)(222,239)(223,235)(224,237)(225,236)(226,232)(227,234)(228,233)(286,287)(289,341)(290,340)(291,342)(292,338)(293,337)(294,339)(295,335)(296,334)(297,336)(298,332)(299,331)(300,333)(301,329)(302,328)(303,330)(304,326)(305,325)(306,327)(307,323)(308,322)(309,324)(310,320)(311,319)(312,321)(313,317)(314,316)(315,318);
s2 := Sym(342)!(  1,175)(  2,176)(  3,177)(  4,172)(  5,173)(  6,174)(  7,226)(  8,227)(  9,228)( 10,223)( 11,224)( 12,225)( 13,220)( 14,221)( 15,222)( 16,217)( 17,218)( 18,219)( 19,214)( 20,215)( 21,216)( 22,211)( 23,212)( 24,213)( 25,208)( 26,209)( 27,210)( 28,205)( 29,206)( 30,207)( 31,202)( 32,203)( 33,204)( 34,199)( 35,200)( 36,201)( 37,196)( 38,197)( 39,198)( 40,193)( 41,194)( 42,195)( 43,190)( 44,191)( 45,192)( 46,187)( 47,188)( 48,189)( 49,184)( 50,185)( 51,186)( 52,181)( 53,182)( 54,183)( 55,178)( 56,179)( 57,180)( 58,232)( 59,233)( 60,234)( 61,229)( 62,230)( 63,231)( 64,283)( 65,284)( 66,285)( 67,280)( 68,281)( 69,282)( 70,277)( 71,278)( 72,279)( 73,274)( 74,275)( 75,276)( 76,271)( 77,272)( 78,273)( 79,268)( 80,269)( 81,270)( 82,265)( 83,266)( 84,267)( 85,262)( 86,263)( 87,264)( 88,259)( 89,260)( 90,261)( 91,256)( 92,257)( 93,258)( 94,253)( 95,254)( 96,255)( 97,250)( 98,251)( 99,252)(100,247)(101,248)(102,249)(103,244)(104,245)(105,246)(106,241)(107,242)(108,243)(109,238)(110,239)(111,240)(112,235)(113,236)(114,237)(115,289)(116,290)(117,291)(118,286)(119,287)(120,288)(121,340)(122,341)(123,342)(124,337)(125,338)(126,339)(127,334)(128,335)(129,336)(130,331)(131,332)(132,333)(133,328)(134,329)(135,330)(136,325)(137,326)(138,327)(139,322)(140,323)(141,324)(142,319)(143,320)(144,321)(145,316)(146,317)(147,318)(148,313)(149,314)(150,315)(151,310)(152,311)(153,312)(154,307)(155,308)(156,309)(157,304)(158,305)(159,306)(160,301)(161,302)(162,303)(163,298)(164,299)(165,300)(166,295)(167,296)(168,297)(169,292)(170,293)(171,294);
poly := sub<Sym(342)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) : 
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope

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